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std::nth_element - cppreference.com

template< class RandomIt >
void nth_element( RandomIt first, RandomIt nth, RandomIt last );

nth_element rearranges elements in [first, last) such that after the rearrangement:

• The element pointed at by nth is changed to whatever element would occur in that position if [first, last) were sorted.
• For every iterator i in [first, nth) and every iterator j in [nth, last), the following condition is met:

is

.

3,4) bool(comp(*j, *i)) is false.

Elements are hypothetically

with respect to

.

3) Elements are hypothetically sorted with respect to comp.

2,4) Same as (1,3), but executed according to policy.

These overloads participate in overload resolution only if all following conditions are satisfied:

If any of the following conditions is satisfied, the behavior is undefined:

• [first, nth) or [nth, last) is not a valid range.

The signature of the comparison function should be equivalent to the following:

bool cmp(const Type1& a, const Type2& b);

While the signature does not need to have const&, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) Type1 and Type2 regardless of value category (thus, Type1& is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy(since C++11)).
The types Type1 and Type2 must be such that an object of type RandomIt can be dereferenced and then implicitly converted to both of them. ​

Given \(\scriptsize N\)N as last - first:

comparisons using

on average.

comparisons using

, and

swaps.

3) \(\scriptsize O(N)\)O(N) applications of the comparator comp on average.

4) \(\scriptsize O(N)\)O(N) applications of the comparator comp, and \(\scriptsize O(N \cdot \log(N))\)O(N·log(N)) swaps.

The overloads with a template parameter named ExecutionPolicy report errors as follows:

• If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined.
• If the algorithm fails to allocate memory, std::bad_alloc is thrown.

See also the implementations in libstdc++, libc++, and MSVC STL.

The algorithm used is typically Introselect although other Selection algorithm with suitable average-case complexity are allowed.

#include <algorithm>
#include <cassert>
#include <functional>
#include <iostream>
#include <numeric>
#include <vector>
 
void printVec(const std::vector<int>& vec)
{
    std::cout << "v = {";
    for (char sep[]{0, ' ', 0}; const int i : vec)
        std::cout << sep << i, sep[0] = ',';
    std::cout << "};\n";
}
 
int main()
{
    std::vector<int> v{5, 10, 6, 4, 3, 2, 6, 7, 9, 3};
    printVec(v);
 
    auto m = v.begin() + v.size() / 2;
    std::nth_element(v.begin(), m, v.end());
    std::cout << "\nThe median is " << v[v.size() / 2] << '\n';
    // The consequence of the inequality of elements before/after the Nth one:
    assert(std::accumulate(v.begin(), m, 0) < std::accumulate(m, v.end(), 0));
    printVec(v);
 
    // Note: comp function changed
    std::nth_element(v.begin(), v.begin() + 1, v.end(), std::greater{});
    std::cout << "\nThe second largest element is " << v[1] << '\n';
    std::cout << "The largest element is " << v[0] << '\n';
    printVec(v);
}

Possible output:

v = {5, 10, 6, 4, 3, 2, 6, 7, 9, 3};
 
The median is 6
v = {3, 2, 3, 4, 5, 6, 10, 7, 9, 6};
 
The second largest element is 9
The largest element is 10
v = {10, 9, 6, 7, 6, 3, 5, 4, 3, 2};

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

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